Deformations of acid-mediated invasive tumors in a model with Allee effect
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285_2025_Article_2209.pdf
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Author(s)
Carter, Paul
Doelman, Arjen
van Heijster, Peter
Levy, Daniel
Maini, Philip
Okey, Erin
Yeung, Paige
Date Issued
May 5, 2025
Journal
Journal of Mathematical Biology
Publisher
Springer Berlin Heidelberg
Citation
Carter, P., Doelman, A., van Heijster, P. et al. Deformations of acid-mediated invasive tumors in a model with Allee effect. J. Math. Biol. 90, 55 (2025).
Version
Final published version
Abstract
We consider a Gatenby–Gawlinski-type model of invasive tumors in the presence of an Allee effect. We describe the construction of bistable one-dimensional traveling fronts using singular perturbation techniques in different parameter regimes corresponding to tumor interfaces with, or without, an acellular gap. By extending the front as a planar interface, we perform a stability analysis to long wavelength perturbations transverse to the direction of front propagation and derive a simple stability criterion for the front in two spatial dimensions. In particular we find that in general the presence of the acellular gap indicates transversal instability of the associated planar front, which can lead to complex interfacial dynamics such as the development of finger-like protrusions and/or different invasion speeds.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s00285-025-02209-w
